Remove objects from the closet and take out the old shelves by unscrewing the mounting screws from the wall, if necessary. A power screwdriver makes this part of the job much easier.
Mark the location for the new shelves on the wall with a pencil by measuring up from the floor 20 inches for the first shelf, then spacing shelves 15 to 20 inches apart up along the wall. Decide how high to make your shelves based on the objects you plan on storing in the linen closet.
Draw a straight, square line using a carpenter's level and pencil across the width of the back wall and side walls using the marks as a guide. This line determines the location of each shelf.
Measure the width of the interior of the closet and, with a power saw, cut 1-by-12 boards to this length. Cut one board for each shelf you will install.
Cut cleats, which will be used to mount the shelving, from 1-by-3 boards to the width of the interior walls. Cut two side cleats, each 9 inches long, for each shelf from the same boards. Paint the boards now, if you plan on painting them, with a paintbrush and interior paint. Allow the boards 12 to 24 hours of drying time.
After detecting the studs with a stud finder, screw the cleats onto the wall right into the studs with 2-inch-long wood screws. Position them so that the top of the cleat is level with the line you drew earlier. If there are no studs, install an anchor in the wall and screw the cleats into the anchor.
Slide the shelves onto the cleats. Drive three screws through the top of the shelving boards and into the cleats: one in back and two on the sides along the edges of the boards.